ARlogo Annu. Rev. Astron. Astrophys. 2004. 42: 603-683
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2.3. Bar-Driven Radial Transport of Gas: The Formation of Rings

Theory (Binney & Tremaine 1987; Sellwood & Wilkinson 1993; Lynden-Bell 1979; 1996) and n-body simulations (Sellwood 1981; Sparke & Sellwood 1987; Pfenniger & Friedli 1991; Athanassoula 2003) show that bars grow by transferring angular momentum to the outer disk, thereby driving spiral structure. As a result, stellar orbits in the bar get more elongated, and the bar grows in amplitude. Its pattern speed slows down.

The essence of the response of gas to a bar is captured in Figure 3 of Simkin, Su, & Schwarz (1980), reproduced here as Figure 5. Outside corotation, gas is driven outward by the angular momentum transfer from bar to disk that makes the bar grow. This gas collects into an "outer ring" near OLR. As discussed earlier, outer rings are oriented perpendicular to the bar when they are interior to OLR; this is the usual situation (Kormendy 1979b; Buta 1995). At radii well inside corotation, gas falls toward the center. This is the gas that is believed to make pseudobulges. Within an annular region around corotation, gas is collected into an "inner ring" near corotation or near the 4:1 ultraharmonic resonance.

Figure 5

Figure 5. Evolution of gas in a rotating oval potential (Simkin, Su, & Schwarz 1980; see also Schwarz 1981, 1984). The gas particles in this sticky-particle n-body model are shown after 2, 3, 5, and 7 bar rotations (top-left through center-left). Arrows show the radii of ILR, corotation, and OLR. Four SB0 or SB0/a galaxies are shown that have outer rings and a lens (NGC 3945) or an inner ring (obvious in ESO 426-2 and in NGC 3081 but poorly developed in NGC 2217). Sources: NGC 3945 - Kormendy (1979b); NGC 2217, NGC 3081 - Buta et al. (2003); ESO 426-2 - Buta & Crocker (1991).

This behavior is seen in a variety of simulations starting as early as Prendergast (1964), Duus & Freeman (1975), and Sørensen et al. (1976). By the early 1980s, there was already an extensive literature on the subject (see Kormendy 19982a and Prendergast 1983 for reviews).

The reason why SB(r) and SB(s) galaxies are different was investigated by Sanders & Tubbs (1980). They simulated the response of gas to an imposed, rigid bar potential that they grew inside a disk galaxy. Examples of the steady-state gas response are shown in Figure 6. In the top two rows of panels, the strength of the bar increases from left to right, either because the ratio of bar mass to disk mass increases (top row), or because the bar gets more elongated (second row). In both cases, weak bars tend to produce an SB(s) response while strong bars produce ring-like structures that resemble SB(r) galaxies. If the bar gets too strong (top-right panel), the result does not look like a real galaxy. The bottom row of simulations explores the effect of varying the bar's pattern speed. Rapid pattern speeds produce dramatically SB(s) structure. Slower pattern speeds in which corotation is near the end of the bar produce inner rings. Very slow pattern rotation (right panel, in which corotation is at 3 bar radii) produce responses that do not look like real galaxies. This is because Omegap is now so small that the radius of ILR is large. Inside ILR, closed gas orbits align perpendicular to the bar. These can never have substantially the same radius as the bar, as they do in the bottom-right simulation in Figure 6. If the response to the bar were perpendicular to the bar over most of the radius of the bar, it would be impossible to make that response add up to a self-consistent bar. Pattern speeds are never so slow that corotation radii are so far out in the disk that the entire bar is inside ILR. This was possible in Sanders & Tubbs (1980) only because the bar was inserted by hand and given a chosen (not a self-consistent) pattern speed. Theoretical arguments tell us that bars end inside or near corotation (Contopoulos 1980; Sellwood & Wilkinson 1993). Observations agree (Kent 1987b; Sempere et al. 1995; Merrifield & Kuijken 1995; Gerssen, Kuijken, & Merrifield 1999, 2003; Debattista & Williams 2001; Gerssen 2002; Debattista, Corsini, & Aguerri 2002; Aguerri, Debattista, & Corsini 2003; Corsini, Debattista, & Aguerri 2003; Corsini, Aguerri, & Debattista 2003; see Elmegreen 1996 for a review) except in late-type galaxies in which V propto r rotation curves imply that the bar is safely clear of ILR anyway (Elmegreen 1996; Elmegreen, Wilcots, & Pisano 1998).

Figure 6

Figure 6. Contours of steady-state gas density in response to a bar (adapted from Sanders & Tubbs 1980, who also show intermediate cases). The bar is horizontal and has a length equal to four axis tick marks. The top row explores the effect of varying the ratio MB / MD of bar mass to disk mass. The second row varies the bar's axial ratio b / a. The third row varies the bar pattern speed, parametrized by the ratio rcor / a of the corotation radius to the disk scale length. The middle column is the same standard model in each row; it approximates an SB(r) galaxy such as NGC 2523 (bottom center). The left panels resemble SB(s) galaxies such as NGC 1300 (bottom left). The right panels carry the parameter sequences to unrealistic extremes; they do not resemble real galaxies.

On the other hand, Sanders & Tubbs (1980) share a number of technical problems with other early simulations of gas response to bars. Their beam scheme (Sanders & Prendergast 1974) code has coarse spatial resolution and unphysical numerical viscosity (see Athanassoula 1992b and Sellwood & Wilkinson 1993). In fact, there are conflicting views on whether viscosity is important at all; Combes (1998) suggests that it is negligible compared to gravitational torques, while Sellwood & Wilkinson 1993 at least consider the possibility that it is important. Gas infall timescales are very uncertain in early simulations.

Still, the main conclusion reached by Sanders & Tubbs (1980) - that weak, fast bars favor SB(s) structure and that strong, slow bars favor SB(r) structure - has largely been confirmed by higher-quality simulations (e.g., Schwarz 1984; Combes & Gerin 1985; Byrd et al. 1994; Englmaier & Gerhard 1997; Salo et al. 1999; Weiner, Sellwood, & Williams 2001a). Well motivated hints of these results came much earlier (Freeman 1970b).

Therefore a widespread feeling has developed that we understand the essentials of ring formation. We share this feeling. However, we also share a concern expressed by K. C. Freeman (private communication): Why do sticky particle simulations make rings so much more clearly than do other (e.g., hydrodynamic) simulations? There may be physics in this. For example, the gas really may be in discrete clouds that collide inelastically. Still, we cannot help but notice that, as simulations have improved, features such as the ones we discuss next - radial dust lanes and nuclear star formation rings - have improved dramatically, but ring formation has made less progress. The subject deserves to be revisited.

Nearly radial dust lanes in bars (see Section 2.1 and Figures 3, 6, 7, 8) are a particularly important diagnostic of SB evolution. They are widely believed to be the observational signatures of shocks that drive gas infall. The idea was proposed by Prendergast (1964); other early studies include Sørensen, Matsuda, & Fujimoto (1976); Roberts, Huntley, & van Albada (1979), and, as discussed above, Sanders & Tubbs (1980).

In an important paper, Athanassoula (1992b) explored the response of inviscid gas to a bar using a high-resolution code. Her main focus was gas shocks and their relation to dust lanes. Typical results are shown in Figure 7. If and only if the mass distribution is centrally concentrated enough to result in an inner Lindblad resonance, the dust lanes are offset in the forward (rotation) direction from the ridge line of the bar. Because of the presence of the x2 orbits - the ones that align perpendicular to the bar inside ILR - the offset is largest near the center, as it is in many galaxies, including the two shown in Figure 7. The models also reproduce the observation that the dust lanes in many bars curve around the center of the galaxy at small radii and become nearly azimuthal. Athanassoula found that the dust lanes are more curved into an open S-shaped structure when the bar is weak; this is confirmed observationally by Knapen, Pérez-Ramírez, & Laine (2002). One shortcoming in the models is that, for weak central concentrations (galaxies with no x2 orbits), the shocks are essentially on the ridge line of the bar. Such dust lanes are not observed. But the main conclusion, as Athanassoula notes, is that "the resemblance between [the models and the observations] is striking".

Figure 7

Figure 7. Comparison of the gas response to a bar (Athanassoula 1992b model 001) with NGC 5236 (left) and NGC 1365 (right). The galaxy images were taked with the VLT and are reproduced courtesy of ESO. In the models, the bar potential is oriented at 45° to the horizontal, parallel to the bar in NGC 5236. The bar axial ratio is 0.4 and its length is approximately half of the box diagonal. The top-right panel shows the velocity field; arrow lengths are proportional to flow velocities. Discontinuities in gas velocity indicate the presence of shocks; these are where the gas density is high in the density map at top-left. High gas densities are identified with dust lanes in the galaxies. The model correctly reproduces the observations (1) that dust lanes are offset in the forward (rotation) direction from the ridge line of the bar; (2) that they are offset by larger amounts nearer the center, and (3) that very near the center, they curve and become nearly azimuthal. As emphasized by the velocity field, the shocks in the model and the dust lanes in the galaxy are signs that the gas loses energy. Therefore it must fall toward the center. In fact, both galaxies have high gas densities and active star formation in their bright centers (e.g., Crosthwaite et al. 2002; Curran et al. 2001a, b).

The important consequence for our discussion is this: Shocks inevitably imply that gas flows toward the center. Because the shocks are nearly radial, gas impacts them at a steep angle. Therefore much of the velocity that is lost in the shock is azimuthal. This robs the gas of energy and forces it to fall toward the center.

Athanassoula estimated that azimuthally averaged gas sinking rates are typically 1 km s-1 and in extreme cases up to ~ 6 km s-1. Since viscosity is not an issue in her models, these estimates are more realistic than earlier ones. And since 1 km s-1 = 1 kpc (109 yr)-1, the implication is that most gas in the inner part of the disk - depleted by star formation but augmented by mass loss during stellar evolution - finds its way to the vicinity of the center over the course of several billion years, if the bar lives that long.

In recent years, simulations have continued to concentrate on these inner regions of barred galaxies where dust lanes and star formation are most important (Friedli & Benz 1993, 1995; Piner, Stone, & Teuben 1995; Lindblad, Lindblad, & Athanassoula 1996; Englmaier & Gerhard 1997; Salo et al. 1999; Weiner, Sellwood, & Williams 2001a; Maciejewski et al. 2002; Regan & Teuben 2003). Details differ, but these conclusions are robust: (1) Everbody agrees that gas flows toward the center. (2) Star formation fed by the inflow is often concentrated in a narrow nuclear ring. (3) The inflow is a result of gravitational torques produced by the bar, but its immediate cause is the shocks. In essence, these are produced because gas accelerates as it approaches and decelerates as it leaves the potential minimum of the bar. So it tends to pile up near the ridge line of the bar. Incoming gas overshoots a little before it plows into the departing gas, so the shocks are nearly radial but offset from the ridge line of the bar in the forward (rotation) direction. More recent simulations confirm Athanassoula's conclusion that offsets happen when the central mass concentration is large enough to allow a "sufficient" range of x2 orbits. The agreement in morphology between the simulated shocks and the observed dust lanes has continued to improve. But there is an even better reason to think that they are connected. Compelling support is provided by the observation of large velocity jumps across the dust lanes (Pence & Blackman 1984; Lindblad, Lindblad, & Athanassoula 1996; Regan, Sheth, & Vogel 1999; Weiner et al. 2001b; and especially Regan, Vogel, & Teuben 1997).

What happens to the infalling gas? Star formation is almost inevitable. The simulations, expectations from the Schmidt (1959) law, observations of young stars in SB nuclei, and star formation indicators (Section 5) all point to enhanced star formation, often in substantial starbursts near the center. Examples are shown in Figure 8. NGC 4314 is a barred galaxy whose central star formation is also illustrated in the Hubble Atlas (Sandage 1961). NGC 1512 is an SB(rs) galaxy whose outer parts are shown in Figure 2. The dust lane in the bar is best seen in the Carnegie Atlas of Galaxies (Sandage & Bedke 1994). NGC 6782 contains an oval disk with an embedded bar; Athanassoula (1992b) predicts very curved dust lanes like those in NGC 6782 when the potential is not very barred. Finally, NGC 4736 is a prototypical unbarred oval galaxy. It is included to illustrate the theme of the next section - barred and oval galaxies evolve similarly.

Figure 8

Figure 8. Nuclear star formation rings in barred and oval galaxies. For NGC 4314, a wide-field view is at top-left; for NGC 4736, the wide-field view is in Figure 2. Sources: NGC 4314 - Benedict et al. (2002); NGC 4736 - NOAO; NGC 1326 - Buta et al. (2000) and Zolt Levay (STScI); NGC 1512 - Maoz et al. (2001); NGC 6782 - Windhorst et al. (2002) and the Hubble Heritage Program.

The examples shown in Figure 8 all have star formation concentrated in tiny rings with mean radii ~ 0.5 kpc (Buta & Crocker 1993). The physics that determines their radii is complicated and not well understood. Many authors suggest that they are caused by gas stalling at ILR or between ILRs (if there are two of them), but this is disputed by Regan & Teuben (2003), and in reality, it is likely that star formation physics and not just inflow physics is involved. In any case, nuclear star formation rings are a reasonably common phenomenon; the most prominent examples have been known for a long time (Morgan 1958; Burbidge & Burbidge 1960, 1962; Sandage 1961; Sérsic & Pastoriza 1965, 1967). Kennicutt (1994, 1998a) provides reviews, contrasting the global star formation in barred galaxies, which is indistinduishable from that in unbarred galaxies, with the nuclear star formation, which is enhanced over that in unbarred galaxies. As predicted by simulations, there is plenty of fuel - the central concentration of molecular gas is higher in barred than in unbarred galaxies (Sakamoto et al. 1999). Additional examples of nuclear star formation rings - and multiple discussions of the best cases - can be found in van der Kruit (1974, 1976); Rubin, Ford, & Peterson (1975); Sandage & Brucato (1979); Hummel, van der Hulst, & Keel (1987); Gerin, Nakai, & Combes (1988); Benedict et al. (1992, 1993, 1996, 2002); Buta (1986a, b, 1988, 1995); Pogge (1989); García-Barreto et al. (1991); Devereux, Kenney, & Young (1992); Buta & Crocker (1993); Pogge & Eskridge (1993: NGC 1819); Forbes et al. (1994a, b); Quillen et al. (1995); Phillips et al. (1996); Buta & Combes (1996); Maoz et al. (1996); Regan et al. (1996); Elmegreen et al. (1997); Colina et al. (1997); Contini et al. (1997); Vega Beltrán et al. (1998); Buta & Purcell (1998); Buta, Crocker, & Byrd (1999); Martini & Pogge (1999); Buta et al. (1999, 2000, 2001); Pérez-Ramírez et al. (2000, 2001); Wong & Blitz (2000, 2001); Waller et al. (2001); Lourenso et al. (2001); Alonso-Herrero, Ryder, & Knapen (2001); Díaz et al. (2002); Knapen, Pérez-Ramírez, & Laine (2002); Windhorst et al. (2002); Erwin & Sparke (2003); Eskridge et al. (2003); Martini et al. (2003a); Combes et al. (2003); Kohno et al. (2003); and Fathi et al. (2003).

Many galaxies discussed in the above papers are barred. The ones that are classified as transition objects (SAB) or as unbarred (SA), have created some uncertainty about how much the star formation depends on bars. However, many SAB and some SA objects are prototypical oval galaxies such as NGC 2903, NGC 3504, NGC 4736 (Figures 2, 8), NGC 5248, and NGC 6951 (see Sandage 1961). We will see in the next section that barred and oval galaxies are essentially equivalent as regards gas inflow, star formation, and pseudobulge building. Section 3.4 suggests that similar evolution happens in unbarred spirals that do not have an ILR.

We argue in later sections, as did some of the above authors, that the nuclear star formation is building pseudobulges. Note that, although the star formation is frequently in a ring, it is not likely to form a ring of stars. If the star-forming ring is associated with ILR, then its radius should change as the central concentration of the galaxy evolves. We expect that the ring of star formation "burns" its way through the pseudobulge as it grows. Also, the spiral dust lanes interior to the star formation rings (Figure 8) suggest that gas continues to sink inside ILR (Elmegreen et al. 1998). Finally, we chose to illustrate star-forming rings, because they most clearly make the connection between star formation and bar-driven secular evolution. However, in many galaxies, the star formation is spread throughout the central region. An example is NGC 1365 (Figure 7; Knapen et al. 1995a, b; Sakamoto et al. 1995; Lindblad 1999).

In summary, a comprehensive picture of the secular evolution of barred galaxies has emerged as simulations of gas response to bars have succeeded with increasing sophistication in matching observations of galaxies. Bars rearrange disk gas to make outer rings, inner rings, and central mass concentrations. SB(s) structure is favored if the bar is weak or rotating rapidly; SB(r) structure is favored if the bar is strong or rotating slowly. Since bars grow stronger and slow down as a result of angular momentum transport to the disk, we conclude that SB(r) galaxies are more mature than SB(s) galaxies. Consistent with this, dust lanes diagnostic of gas inflow are seen in SB(s) galaxies but only rarely in SB(r) galaxies. By the time an inner ring is well developed, the gas inside it has been depleted. Embedded in this larger picture is the most robust conclusion of both the modeling and the observations - that a substantial fraction of the disk gas falls down to small galactocentric radii in not more than a few billion years. Star formation is the expected result, and star formation plausibly associated with bars (concentrated near resonance rings) is seen. These results provide part of the motivation for our conclusion that secular evolution builds pseudobulges, that is, dense but disk-like central components in spiral and S0 galaxies that are not made by galaxy mergers.

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